The photoabsorption spectra of single-shell icosahedral fullerenes are investigated in the region of the strongest diffuse interstellar band at 4430 Å. According to Hückel and Pariser-Parr-Pople models, several fullerenes (C80, C240, C320, and C540) present transitions in the vicinity of this band. The same semiempirical models also predict a high density of transitions in the UV that may explain the 2175 Å bump in the extinction curve of the interstellar medium. It appears that fullerenes could be responsible of these two major features of interstellar absorption. Using the theoretical cross sections and available empirical data on the 4430 Å band, we estimate abundances of ~0.05 molecules per million hydrogen atoms for these fullerenes in regions of the interstellar medium with an excess color index of E(B-V)=1.0.